糖心TV

Sam Brand

Speaker: Bartek Waclaw (Edinburgh)

Title: A dynamical phase transition in a model for evolution with migration

Biological dispersal---the movement of organisms between habitats---is a ubiquitous phenomenon with important and wide-ranging consequences. In the natural environment, organisms expand their ranges, colonise new habitats, and can undergo speciation if they become spatially isolated. Therefore, dispersal plays a key role in determining spatial and temporal patterns of genetic diversity. It has been pointed out recently, that migration from a favourable habitat to an unfavourable one can explain the genetics of some pathogenic microbes and viruses. However, despite its importance, a general understanding of how migration affects mutation-selection balance in microbial systems is lacking. In particular, one would like to know how migration changes the proportions of different genotypes in the evolving population. Here I will discuss a simple model for evolution of asexual organisms in two different habitats, with different fitness landscapes, coupled through one-way migration. The key finding is a dynamical phase transition at a critical value of the migration rate. The time to reach steady state diverges at this critical migration rate. Above the transition, the population is dominated by immigrants from the primary habitat. Below the transition, the genetic composition of the population is highly non-trivial, with multiple coexisting quasi-species which are not native to either habitat. Using results from localization theory, I will show that the critical migration rate may be very small --- demonstrating that evolutionary outcomes can be very sensitive to even a small amount of migration.